/*
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
*/

P.<x> = PolynomialRing(QQ)
g = P([-1, 3, 4, -5, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([27, 27, w^4 - w^3 - 5*w^2 + 4*w + 1])

primes_array = [
[3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[9, 3, -w^4 + 5*w^2 - 3],\
[9, 3, -w^4 + w^3 + 5*w^2 - 3*w - 2],\
[13, 13, -w^4 + w^3 + 4*w^2 - 3*w - 1],\
[17, 17, w^4 - w^3 - 5*w^2 + 3*w + 1],\
[19, 19, -w^3 + w^2 + 4*w - 2],\
[23, 23, -w^2 + 3],\
[31, 31, w^3 - 4*w + 2],\
[32, 2, 2],\
[37, 37, w^3 - 3*w - 1],\
[53, 53, -2*w^4 + w^3 + 9*w^2 - 3*w - 2],\
[59, 59, -w^4 + 5*w^2 + w - 4],\
[61, 61, -w^4 + w^3 + 5*w^2 - 4*w],\
[67, 67, -w^4 + 6*w^2 + 2*w - 4],\
[71, 71, 2*w^4 - w^3 - 9*w^2 + 4*w + 5],\
[79, 79, 2*w^4 - w^3 - 10*w^2 + 2*w + 7],\
[83, 83, -w^4 + 2*w^3 + 5*w^2 - 7*w - 2],\
[83, 83, -w^4 + w^3 + 4*w^2 - 3*w + 3],\
[83, 83, w^4 - w^3 - 5*w^2 + 4*w - 1],\
[83, 83, -w^4 + w^3 + 4*w^2 - 4*w - 2],\
[83, 83, -2*w^4 + w^3 + 9*w^2 - 3*w - 5],\
[97, 97, -w^4 - w^3 + 6*w^2 + 4*w - 4],\
[101, 101, -w^4 + 4*w^2 + 2*w - 2],\
[107, 107, -2*w^4 + w^3 + 11*w^2 - 3*w - 7],\
[127, 127, w^3 - w^2 - 4*w],\
[131, 131, w^4 - w^3 - 4*w^2 + 2*w - 1],\
[137, 137, w^4 - w^3 - 6*w^2 + 3*w + 3],\
[139, 139, -2*w^4 + w^3 + 9*w^2 - 3*w + 1],\
[157, 157, 2*w^4 - w^3 - 9*w^2 + 4*w + 2],\
[163, 163, -w^2 - 2*w + 3],\
[167, 167, w^4 - 5*w^2 + 2*w + 1],\
[169, 13, -2*w^4 + 2*w^3 + 9*w^2 - 7*w - 5],\
[169, 13, w^4 - 2*w^3 - 5*w^2 + 8*w + 2],\
[191, 191, 2*w^4 - w^3 - 9*w^2 + 3*w + 4],\
[193, 193, 2*w^4 - 2*w^3 - 8*w^2 + 7*w],\
[199, 199, -w^4 + 2*w^3 + 5*w^2 - 9*w - 3],\
[211, 211, -3*w^4 + w^3 + 13*w^2 - 2*w - 1],\
[227, 227, 2*w^3 - w^2 - 9*w + 1],\
[233, 233, -w^3 + w^2 + 4*w + 1],\
[251, 251, -3*w^4 + 14*w^2 + w - 2],\
[257, 257, -2*w^4 + 2*w^3 + 10*w^2 - 6*w - 5],\
[257, 257, -w^4 + w^3 + 5*w^2 - 6*w - 1],\
[257, 257, 2*w^4 - 2*w^3 - 11*w^2 + 9*w + 9],\
[257, 257, -2*w^4 + 2*w^3 + 9*w^2 - 6*w - 3],\
[257, 257, 2*w^4 - w^3 - 10*w^2 + 5*w + 5],\
[269, 269, -w^4 + 2*w^3 + 4*w^2 - 6*w - 2],\
[271, 271, -w^4 + 4*w^2 + w - 3],\
[277, 277, -2*w^4 + 9*w^2 + w - 4],\
[281, 281, w^4 - w^3 - 3*w^2 + 3*w - 4],\
[283, 283, 2*w^4 - 3*w^3 - 8*w^2 + 13*w],\
[289, 17, -w^4 + w^3 + 7*w^2 - 5*w - 5],\
[289, 17, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 6],\
[293, 293, -2*w^4 + 11*w^2 - 7],\
[317, 317, w^3 - 6*w],\
[337, 337, -w^4 + 2*w^3 + 5*w^2 - 9*w - 1],\
[337, 337, w^4 - 2*w^3 - 5*w^2 + 6*w + 3],\
[337, 337, -w^4 + w^3 + 5*w^2 - 4*w - 6],\
[337, 337, -2*w^3 + 8*w + 1],\
[337, 337, w^2 + w - 5],\
[347, 347, -2*w^4 + w^3 + 9*w^2 - 5*w - 3],\
[349, 349, 3*w^4 - 2*w^3 - 13*w^2 + 8*w + 2],\
[353, 353, w^4 - 3*w^3 - 4*w^2 + 12*w + 2],\
[359, 359, 2*w^3 - w^2 - 7*w + 3],\
[361, 19, w^4 - 2*w^3 - 4*w^2 + 7*w + 3],\
[361, 19, w^4 - w^3 - 3*w^2 + 3*w - 3],\
[367, 367, -2*w^4 + w^3 + 9*w^2 - w - 2],\
[379, 379, -2*w^3 + w^2 + 7*w + 2],\
[379, 379, -2*w^4 + w^3 + 10*w^2 - 4*w],\
[379, 379, 2*w^3 - w^2 - 6*w - 2],\
[379, 379, -2*w^3 + 2*w^2 + 6*w - 3],\
[379, 379, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 6],\
[383, 383, 2*w^4 + w^3 - 10*w^2 - 7*w + 4],\
[383, 383, -2*w^3 + w^2 + 10*w],\
[383, 383, w^3 + w^2 - 5*w - 1],\
[383, 383, 3*w^4 + 3*w^3 - 15*w^2 - 15*w + 4],\
[383, 383, -2*w^4 + 3*w^3 + 10*w^2 - 10*w - 2],\
[389, 389, 3*w^4 - w^3 - 14*w^2 + 3*w + 3],\
[397, 397, w^4 - 6*w^2 - 2*w + 5],\
[397, 397, w^4 - 2*w^3 - 2*w^2 + 6*w - 5],\
[397, 397, 2*w^4 - 2*w^3 - 11*w^2 + 10*w + 6],\
[397, 397, w^4 - w^3 - 3*w^2 + 4*w - 6],\
[397, 397, w^3 + w^2 - 3*w - 4],\
[401, 401, w^3 - w^2 - 6*w + 3],\
[401, 401, -w^4 + 4*w^2 + 2*w - 3],\
[401, 401, -w^4 + 6*w^2 - w - 7],\
[421, 421, -w^4 - w^3 + 5*w^2 + 5*w - 4],\
[421, 421, -w^4 + w^3 + 6*w^2 - 3*w - 2],\
[421, 421, -w^4 - w^3 + 6*w^2 + 6*w - 5],\
[421, 421, 3*w^4 - w^3 - 15*w^2 + w + 10],\
[421, 421, 2*w^4 - 9*w^2 + 2*w + 4],\
[431, 431, 2*w^4 - 11*w^2 - 2*w + 11],\
[439, 439, 2*w^4 - 3*w^3 - 9*w^2 + 10*w + 6],\
[443, 443, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 2],\
[449, 449, -w^4 + 2*w^3 + 5*w^2 - 6*w - 4],\
[461, 461, 3*w^4 - 4*w^3 - 14*w^2 + 14*w + 5],\
[463, 463, w^3 - 6*w - 1],\
[467, 467, 3*w^4 - 3*w^3 - 13*w^2 + 10*w],\
[487, 487, 3*w^4 - w^3 - 14*w^2 + w + 3],\
[487, 487, 2*w^2 - w - 4],\
[487, 487, -2*w^4 + 2*w^3 + 9*w^2 - 8*w - 5],\
[487, 487, 2*w^4 - 10*w^2 - 3*w + 4],\
[487, 487, -2*w^4 + w^3 + 8*w^2 - 3*w - 1],\
[499, 499, -w^4 + 2*w^3 + 4*w^2 - 8*w - 2],\
[499, 499, -2*w^4 + w^3 + 10*w^2 - w - 9],\
[499, 499, -w^3 - 2*w^2 + 2*w + 5],\
[499, 499, -w^4 + 4*w^2 + 4*w],\
[499, 499, -2*w^4 + w^3 + 12*w^2 - 4*w - 9],\
[509, 509, 3*w^4 - 2*w^3 - 16*w^2 + 6*w + 9],\
[521, 521, -2*w^4 + w^3 + 10*w^2 - 5*w - 4],\
[523, 523, w - 4],\
[529, 23, -w^3 + 2*w^2 + 4*w - 4],\
[529, 23, w^4 + 2*w^3 - 6*w^2 - 11*w + 4],\
[569, 569, -2*w^4 + 11*w^2 - 10],\
[571, 571, -2*w^4 + w^3 + 10*w^2 - 3*w - 2],\
[593, 593, -2*w^4 + 3*w^3 + 10*w^2 - 11*w - 8],\
[613, 613, -2*w^3 + 2*w^2 + 9*w - 5],\
[617, 617, -2*w^4 + 10*w^2 - w - 7],\
[631, 631, -2*w^4 + 2*w^3 + 7*w^2 - 8*w + 3],\
[641, 641, -2*w^4 + 2*w^3 + 8*w^2 - 9*w + 3],\
[643, 643, -3*w^4 + w^3 + 13*w^2 - w + 1],\
[643, 643, w^4 + w^3 - 3*w^2 - 6*w - 2],\
[643, 643, -w^4 - w^3 + 6*w^2 + 3*w - 4],\
[643, 643, 2*w^4 - w^3 - 10*w^2 + 4*w + 1],\
[643, 643, 2*w^4 - 2*w^3 - 8*w^2 + 6*w + 5],\
[647, 647, -2*w^3 + w^2 + 6*w - 4],\
[659, 659, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 10],\
[661, 661, 2*w^4 + 3*w^3 - 11*w^2 - 14*w + 6],\
[673, 673, w^4 - 3*w^3 - 3*w^2 + 10*w - 1],\
[683, 683, w^4 - 2*w^3 - 4*w^2 + 6*w - 4],\
[701, 701, w^3 - w^2 - 2*w + 4],\
[727, 727, -w^4 + 6*w^2 + 2*w - 7],\
[743, 743, w^4 - w^3 - 7*w^2 + 5*w + 9],\
[769, 769, w^4 + 2*w^3 - 5*w^2 - 9*w + 4],\
[787, 787, w^4 + w^3 - 7*w^2 - 3*w + 5],\
[797, 797, -2*w^4 - w^3 + 10*w^2 + 4*w - 4],\
[797, 797, w^4 - 3*w^3 - 5*w^2 + 12*w + 5],\
[797, 797, -3*w^4 + 2*w^3 + 13*w^2 - 8*w],\
[797, 797, -w^4 + w^3 + 3*w^2 - 5*w - 1],\
[797, 797, 2*w^4 - 11*w^2 + 2*w + 7],\
[809, 809, -4*w^4 + 2*w^3 + 18*w^2 - 6*w + 1],\
[809, 809, 3*w^4 - 3*w^3 - 14*w^2 + 11*w + 8],\
[809, 809, w^4 - 2*w^3 - 2*w^2 + 8*w - 4],\
[809, 809, 2*w^4 - 8*w^2 - 2*w + 3],\
[809, 809, 2*w^4 - 3*w^3 - 9*w^2 + 13*w + 4],\
[821, 821, -2*w^4 + 2*w^3 + 8*w^2 - 6*w + 3],\
[823, 823, -2*w^4 + 3*w^3 + 8*w^2 - 12*w - 1],\
[829, 829, 2*w^4 - 3*w^3 - 10*w^2 + 13*w + 4],\
[839, 839, -2*w^4 + 12*w^2 - w - 10],\
[863, 863, 2*w^4 - w^3 - 9*w^2 + 5],\
[877, 877, -w^4 + w^3 + 5*w^2 - 5*w - 7],\
[881, 881, 2*w^4 - w^3 - 9*w^2 + w - 1],\
[887, 887, 3*w^4 - 3*w^3 - 15*w^2 + 11*w + 6],\
[907, 907, -3*w^4 + w^3 + 13*w^2 - w - 5],\
[919, 919, w^4 + w^3 - 3*w^2 - 5*w - 3],\
[929, 929, 2*w^4 - 3*w^3 - 10*w^2 + 9*w + 4],\
[937, 937, -2*w^4 + 10*w^2 + 3*w - 7],\
[941, 941, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\
[961, 31, 2*w^4 + 2*w^3 - 10*w^2 - 12*w + 5],\
[961, 31, -w^4 + 5*w^2 - w - 7],\
[967, 967, -2*w^4 + w^3 + 9*w^2 - 3*w + 2],\
[991, 991, -3*w^4 + w^3 + 15*w^2 - 4*w - 5],\
[997, 997, -3*w^4 + 15*w^2 - 5],\
[997, 997, 2*w^4 - w^3 - 9*w^2 + 6*w + 2],\
[997, 997, 2*w^4 - w^3 - 11*w^2 + w + 7],\
[997, 997, 2*w^3 - 5*w - 1],\
[997, 997, 2*w^4 - 3*w^3 - 6*w^2 + 5*w + 1]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 - 4*x^4 - 13*x^3 + 44*x^2 + 42*x - 118
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, e^3 - 4*e^2 - 7*e + 23, 1/8*e^4 - 7/8*e^3 + 13/2*e - 9/4, -1/4*e^4 + 7/4*e^3 - e^2 - 10*e + 25/2, -1/4*e^4 + 3/4*e^3 + 3*e^2 - 4*e - 7/2, 1/4*e^4 - 7/4*e^3 + 2*e^2 + 10*e - 45/2, 1/4*e^4 - 7/4*e^3 + e^2 + 9*e - 25/2, -1/8*e^4 - 1/8*e^3 + 4*e^2 + 1/2*e - 59/4, 5/8*e^4 - 19/8*e^3 - 6*e^2 + 29/2*e + 35/4, e^3 - 5*e^2 - 4*e + 26, -5/8*e^4 + 27/8*e^3 + e^2 - 39/2*e + 69/4, 5/8*e^4 - 19/8*e^3 - 6*e^2 + 25/2*e + 67/4, -1/4*e^4 + 3/4*e^3 + 3*e^2 - 4*e - 13/2, -7/8*e^4 + 25/8*e^3 + 8*e^2 - 37/2*e - 33/4, -1/8*e^4 + 7/8*e^3 - 7/2*e + 13/4, -2*e^3 + 9*e^2 + 14*e - 48, 1/2*e^4 - 7/2*e^3 + 4*e^2 + 20*e - 42, 5/4*e^4 - 19/4*e^3 - 11*e^2 + 25*e + 39/2, -1/4*e^4 + 7/4*e^3 - e^2 - 10*e + 25/2, -e^4 + 4*e^3 + 7*e^2 - 19*e - 3, 1/8*e^4 + 1/8*e^3 - 3*e^2 - 1/2*e + 51/4, -3/8*e^4 - 11/8*e^3 + 14*e^2 + 23/2*e - 257/4, -3/8*e^4 + 5/8*e^3 + 6*e^2 - 11/2*e - 45/4, -5/8*e^4 + 27/8*e^3 - 35/2*e + 73/4, -3/2*e^4 + 11/2*e^3 + 13*e^2 - 31*e - 13, e^3 - 5*e^2 - e + 32, 3/4*e^4 - 9/4*e^3 - 11*e^2 + 14*e + 67/2, 5/8*e^4 - 27/8*e^3 + 31/2*e - 85/4, -1/2*e^4 + 5/2*e^3 - e^2 - 11*e + 33, -3/4*e^4 + 9/4*e^3 + 8*e^2 - 12*e - 43/2, -3/4*e^4 + 9/4*e^3 + 6*e^2 - 7*e - 9/2, 1/4*e^4 - 3/4*e^3 - 3*e^2 + 5*e + 31/2, 13/8*e^4 - 75/8*e^3 - 2*e^2 + 117/2*e - 141/4, 1/2*e^4 - 1/2*e^3 - 11*e^2 + 4*e + 48, -3/4*e^4 + 9/4*e^3 + 10*e^2 - 13*e - 53/2, 1/4*e^4 + 1/4*e^3 - 7*e^2 - 7*e + 61/2, e^3 - 2*e^2 - 10*e + 2, e^4 - 3*e^3 - 9*e^2 + 9*e + 17, 9/8*e^4 - 47/8*e^3 - e^2 + 59/2*e - 161/4, -3/4*e^4 + 9/4*e^3 + 9*e^2 - 15*e - 33/2, -1/4*e^4 - 13/4*e^3 + 19*e^2 + 22*e - 177/2, 3/8*e^4 - 5/8*e^3 - 6*e^2 - 1/2*e + 105/4, -9/8*e^4 + 63/8*e^3 - 4*e^2 - 99/2*e + 229/4, -9/8*e^4 + 31/8*e^3 + 11*e^2 - 43/2*e - 59/4, 13/8*e^4 - 51/8*e^3 - 13*e^2 + 69/2*e + 59/4, -1/8*e^4 + 31/8*e^3 - 13*e^2 - 61/2*e + 293/4, 3/8*e^4 + 3/8*e^3 - 9*e^2 - 17/2*e + 141/4, -1/2*e^4 + 3/2*e^3 + 5*e^2 - 3*e, 1/4*e^4 + 1/4*e^3 - 9*e^2 - 2*e + 97/2, -3/8*e^4 + 13/8*e^3 + e^2 - 13/2*e + 67/4, 1/2*e^4 - 5/2*e^3 + 2*e^2 + 6*e - 31, -9/8*e^4 + 39/8*e^3 + 8*e^2 - 57/2*e - 23/4, 1/4*e^4 + 9/4*e^3 - 17*e^2 - 15*e + 191/2, -e^4 + 25*e^2 + 9*e - 106, -2*e^3 + 8*e^2 + 10*e - 41, 1/4*e^4 - 7/4*e^3 + 3*e^2 + 6*e - 17/2, 3/2*e^4 - 15/2*e^3 - 5*e^2 + 42*e - 23, 3/4*e^4 + 11/4*e^3 - 28*e^2 - 20*e + 237/2, -3/4*e^4 + 5/4*e^3 + 10*e^2 + 4*e - 53/2, -e^4 + e^3 + 23*e^2 - 7*e - 86, -7/8*e^4 + 41/8*e^3 - 71/2*e + 143/4, 15/8*e^4 - 65/8*e^3 - 10*e^2 + 95/2*e - 71/4, 1/4*e^4 + 5/4*e^3 - 7*e^2 - 14*e + 31/2, 1/8*e^4 + 25/8*e^3 - 15*e^2 - 57/2*e + 319/4, 9/8*e^4 + 1/8*e^3 - 26*e^2 - 15/2*e + 407/4, 5/8*e^4 - 35/8*e^3 + 6*e^2 + 41/2*e - 221/4, 9/8*e^4 - 7/8*e^3 - 24*e^2 + 11/2*e + 291/4, -17/8*e^4 + 79/8*e^3 + 11*e^2 - 111/2*e + 41/4, 1/4*e^4 + 29/4*e^3 - 35*e^2 - 50*e + 369/2, e^4 - 5*e^3 - 5*e^2 + 35*e - 6, 7/8*e^4 - 41/8*e^3 - 2*e^2 + 65/2*e - 39/4, -4*e^3 + 17*e^2 + 25*e - 101, -9/8*e^4 + 47/8*e^3 + 6*e^2 - 77/2*e + 57/4, -5/4*e^4 + 31/4*e^3 - e^2 - 46*e + 99/2, -1/8*e^4 - 1/8*e^3 + 4*e^2 + 7/2*e - 131/4, -5/8*e^4 - 13/8*e^3 + 21*e^2 + 31/2*e - 347/4, 5/4*e^4 - 7/4*e^3 - 23*e^2 + 3*e + 159/2, 9/8*e^4 - 31/8*e^3 - 10*e^2 + 41/2*e + 55/4, 9/4*e^4 - 39/4*e^3 - 16*e^2 + 56*e + 23/2, 7/8*e^4 - 41/8*e^3 + 3*e^2 + 51/2*e - 167/4, -7/8*e^4 - 7/8*e^3 + 25*e^2 + 19/2*e - 465/4, 3/2*e^4 - 7/2*e^3 - 22*e^2 + 11*e + 73, -27/8*e^4 + 117/8*e^3 + 22*e^2 - 171/2*e - 13/4, 1/8*e^4 + 9/8*e^3 - 7*e^2 - 15/2*e + 71/4, -3/4*e^4 + 33/4*e^3 - 15*e^2 - 55*e + 225/2, -3/8*e^4 - 19/8*e^3 + 18*e^2 + 35/2*e - 357/4, 11/8*e^4 - 21/8*e^3 - 24*e^2 + 31/2*e + 341/4, -3/8*e^4 + 5/8*e^3 + 7*e^2 - 7/2*e - 61/4, -1/2*e^4 + 11/2*e^3 - 12*e^2 - 37*e + 97, -13/8*e^4 + 91/8*e^3 - 5*e^2 - 145/2*e + 325/4, 23/8*e^4 - 105/8*e^3 - 14*e^2 + 153/2*e - 87/4, 0, 3/8*e^4 - 29/8*e^3 + 7*e^2 + 41/2*e - 211/4, 1/8*e^4 - 23/8*e^3 + 7*e^2 + 35/2*e - 165/4, -3/4*e^4 + 17/4*e^3 - e^2 - 27*e + 47/2, -3/2*e^4 + 17/2*e^3 + 4*e^2 - 52*e + 32, 9/8*e^4 - 63/8*e^3 + 6*e^2 + 91/2*e - 333/4, -2*e^4 + 6*e^3 + 23*e^2 - 27*e - 64, 5*e^3 - 18*e^2 - 36*e + 84, -9/8*e^4 + 15/8*e^3 + 23*e^2 - 17/2*e - 359/4, e^4 - 3*e^3 - 14*e^2 + 17*e + 40, -3/4*e^4 + 1/4*e^3 + 17*e^2 - 4*e - 117/2, -1/2*e^4 + 3/2*e^3 + 6*e^2 - 32, 1/4*e^4 + 5/4*e^3 - 15*e^2 - 5*e + 155/2, 3/4*e^4 - 33/4*e^3 + 15*e^2 + 53*e - 213/2, 3/4*e^4 - 13/4*e^3 - 5*e^2 + 18*e + 55/2, 1/8*e^4 + 9/8*e^3 - 9*e^2 - 21/2*e + 223/4, -5/4*e^4 + 19/4*e^3 + 8*e^2 - 22*e + 21/2, 7/8*e^4 - 49/8*e^3 + 4*e^2 + 85/2*e - 127/4, 11/4*e^4 - 33/4*e^3 - 33*e^2 + 48*e + 153/2, -9/8*e^4 + 39/8*e^3 + 6*e^2 - 45/2*e - 19/4, -1/8*e^4 - 17/8*e^3 + 15*e^2 + 5/2*e - 319/4, -1/2*e^4 + 3/2*e^3 + 6*e^2 - 12*e - 5, -e^4 + 2*e^3 + 18*e^2 - 5*e - 80, 5/4*e^4 - 15/4*e^3 - 17*e^2 + 15*e + 115/2, -1/2*e^4 + 5/2*e^3 - 16*e + 47, 5/4*e^4 - 39/4*e^3 + 8*e^2 + 65*e - 137/2, -1/2*e^4 + 3/2*e^3 + 2*e^2 + 3*e - 3, e^4 - 5*e^3 - 2*e^2 + 23*e - 48, 1/2*e^4 - 15/2*e^3 + 20*e^2 + 45*e - 149, -13/8*e^4 + 43/8*e^3 + 19*e^2 - 45/2*e - 251/4, -9/8*e^4 + 47/8*e^3 + 5*e^2 - 79/2*e + 97/4, 3/2*e^4 - 15/2*e^3 - 4*e^2 + 39*e - 51, -7/8*e^4 + 65/8*e^3 - 13*e^2 - 107/2*e + 399/4, -5/2*e^4 + 19/2*e^3 + 21*e^2 - 56*e - 11, 11/4*e^4 - 45/4*e^3 - 21*e^2 + 69*e + 21/2, 7/8*e^4 - 49/8*e^3 + 4*e^2 + 61/2*e - 247/4, -1/2*e^4 + 3/2*e^3 + 7*e^2 - 15*e - 35, 9/4*e^4 - 43/4*e^3 - 11*e^2 + 61*e - 53/2, -7/8*e^4 + 65/8*e^3 - 13*e^2 - 79/2*e + 423/4, -17/8*e^4 + 71/8*e^3 + 17*e^2 - 107/2*e - 7/4, -11/8*e^4 + 61/8*e^3 - e^2 - 85/2*e + 307/4, -13/8*e^4 + 51/8*e^3 + 18*e^2 - 93/2*e - 143/4, 23/8*e^4 - 89/8*e^3 - 23*e^2 + 119/2*e + 97/4, 7/8*e^4 + 15/8*e^3 - 32*e^2 - 9/2*e + 573/4, 15/8*e^4 - 97/8*e^3 + 3*e^2 + 139/2*e - 327/4, 25/8*e^4 - 63/8*e^3 - 43*e^2 + 69/2*e + 527/4, 11/4*e^4 - 65/4*e^3 + 2*e^2 + 92*e - 239/2, 7/8*e^4 - 57/8*e^3 + 8*e^2 + 87/2*e - 283/4, -5/8*e^4 + 3/8*e^3 + 13*e^2 - 9/2*e - 159/4, -13/8*e^4 + 107/8*e^3 - 19*e^2 - 161/2*e + 645/4, e^4 - 4*e^3 - 7*e^2 + 25*e - 9, 11/4*e^4 - 57/4*e^3 - 11*e^2 + 87*e - 27/2, -5/2*e^4 + 25/2*e^3 + 13*e^2 - 80*e + 6, 1/2*e^4 - 3/2*e^3 - 9*e^2 + 12*e + 21, -2*e^4 + 7*e^3 + 21*e^2 - 41*e - 40, -7/8*e^4 + 33/8*e^3 - 3*e^2 - 21/2*e + 191/4, -5/8*e^4 + 83/8*e^3 - 29*e^2 - 125/2*e + 705/4, 9/4*e^4 - 51/4*e^3 + 2*e^2 + 71*e - 169/2, 23/8*e^4 - 145/8*e^3 + 2*e^2 + 229/2*e - 351/4, -5/8*e^4 + 11/8*e^3 + 12*e^2 - 5/2*e - 179/4, 3/2*e^4 - 17/2*e^3 - 3*e^2 + 60*e - 15, -1/8*e^4 - 9/8*e^3 + 12*e^2 + 3/2*e - 263/4, -1/8*e^4 - 33/8*e^3 + 19*e^2 + 69/2*e - 419/4, 1/4*e^4 + 5/4*e^3 - 11*e^2 - 12*e + 95/2, -7/4*e^4 + 69/4*e^3 - 29*e^2 - 102*e + 465/2, -11/8*e^4 + 37/8*e^3 + 17*e^2 - 69/2*e - 157/4, 9/8*e^4 - 47/8*e^3 - 2*e^2 + 47/2*e - 113/4, -3/8*e^4 + 5/8*e^3 + 7*e^2 - 19/2*e - 97/4, 3/2*e^4 - 15/2*e^3 - 6*e^2 + 42*e - 31, -21/8*e^4 + 115/8*e^3 + 4*e^2 - 165/2*e + 269/4, -5/2*e^4 + 17/2*e^3 + 27*e^2 - 55*e - 48, e^4 - 3*e^3 - 12*e^2 + 20*e + 68, 11/4*e^4 - 29/4*e^3 - 40*e^2 + 35*e + 227/2, 1/2*e^4 + 7/2*e^3 - 29*e^2 - 32*e + 161]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3])] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]